In this paper, the Symmetric Galerkin Boundary Element Method for Linear Elastic Fracture Mechanics is extended to non-linear cohesive cracks propagating through homogeneous linear elastic isotropic media. The cohesive model adopted is based on the concept of free energy density per unit undeformed area. The corresponding constitutive cohesive equations present a softening branch which induces a potential instability. Thus, a suitable solution algorithm capable of following the growth of the cohesive zone is needed, and in the present work the numerical simulation is controlled by an arc-length method combined with a Newton-Raphson algorithm for the iterative solution of nonlinear equations. The Boundary ElementMethod is very attractive for modeling cohesive crack problems as all nonlinearities are located on the boundaries of linear elastic domains. Moreover a Galerkin approximation scheme, applied to a suitable symmetric boundary integral equation formulation, ensures an easy and efficient treatment of cracks in homogeneous media and an excellent convergence behavior of the numerical solution. The cohesive zone model is applied to simulate a pure mode I crack propagation in concrete. Numerical results for three-point bending test are used to check the numerical results for mode I and are compared with some numerical results obtained by FEM analysis found in the literature.